基于局部模态的约束子结构模型修正法

ISOLATED SUBSTRUCTURE MODEL UPDATING BASED ON LOCAL MODE

针对局部子结构为修正对象的情况提出了约束子结构修正法,实现只利用整体结构模态中对应子结构部分的模态即可以修正子结构模型.由脉冲响应结合特征系统实现法识别出子结构的低阶模态;结合识别的模态和整体结构理论模型的高阶模态构造整体结构对应子结构位置的柔度矩阵;利用柔度矩阵的物理意义,在子结构的边界上施加数值支座,把子结构从整体结构中隔离出来成为约束子结构,同时构造出约束子结构的柔度矩阵;利用灵敏度的方法根据构造出的约束子结构柔度矩阵,优化修正约束子结构,即间接等效地修正子结构模型.通过一个平面桁架结构验证了约束子结构模型修正法的可行性与有效性,即使在5%或10%的噪声影响下,仍能得到满意的修正结果.

Modal updating is a crucial problem in Structure Health Monitoring （SHM） and has strongly attracted researchers＇ attentions. Recently the structures have been becoming much huger and more complex, so it＇s getting harder to update the global structural model precisely using the classical model updating methods. In general, only some local substructure model is important and it is not necessary to update the whole structure. Therefore the substructure technologies are important for that they require only few sensors and the local dynamic information to accurately update the interested substructure model. Usually the updating of the element stiffness is enough to reflect the damage and the structural dynamic performance. This paper proposes a concept of the Isolated Substructure. It aims at updating local substructure element stiffness only by the relative mode at the substructure location. The present Isolated Substructure refers to a new structure formed by isolating the substructure from the global structure. Then the substructure can be updated indirectly through updating the Isolated Substructure, such that the optimizing variables become much less and the convergent speed is fastened. The key process of this method is to construct the flexibility matrix of the Isolated Substructure by measured data. First the lower order frequencies and shape modes of the substructure are identified from the measured impulse response by utilizing Eigensystem Realization Algorithm （ERA）, and the relative modal masses are estimated by Least Square Method （LSM）; Second, according to its independence and convergence properties, the flexibility matrix corresponding to the substructure can be approximately constructed by the identified lower order modes and be improved by the calculated higher order modes from the theoretical model; and then utilizing the concept of the flexibility matrix, the substructure is isolated from the global structure through applying numerical supporting on the substructure boundary; synchronously the flexibility matrix of the Isolated Substructure is constructed from the advanced obtained flexibility matrix of the global structure, and is used to update the Isolated Substructure, that is, to equally update the substructure. The optimization method based on sensitivity idea is adopted, and the relative formulas are deduced. It makes the iteration and convergence faster. A numerical example of a plane truss separately with 5% or 10% rms Gaussian measurement error validates that the substructure can be updated effectively by the Isolated Substructure model updating method.